Polytope of Type {8,6} with group SmallGroup(960,10877)

Overview

Group: SmallGroup(960,10877)
Rank: 3
Schläfli Type: {8,6}
Vertices, edges, …: 80, 240, 60
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 12
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{4,6}*480

4-fold

8-fold

{4,6}*120

120-fold

{2,2}*8

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 2

30 facets

30 of {8}*16

40 vertex figures

40 of {6}*12

P/N, where N=<s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2> of order 3

20 facets

20 of {8}*16

32 vertex figures

24 of {6}*12
8 of {2}*4

P/N, where N=<s0*(s2*s1)^2*s0*s1*s2*s1*s0*s1, (s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 6

10 facets

10 of {8}*16

16 vertex figures

12 of {6}*12
4 of {2}*4

Representations

Permutation Representation (GAP)

s0 := ( 1, 5)( 2,41)( 3,32)( 4,54)( 6,43)( 7,18)( 9,14)(10,47)(11,16)(12,64)(13,44)(15,19)(17,62)(20,30)(21,53)(22,27)(23,36)(24,34)(25,29)(26,55)(28,39)(31,75)(33,78)(35,77)(37,76)(38,73)(42,80)(45,70)(46,61)(48,72)(49,66)(51,69)(52,79)(56,58)(57,60)(59,71)(63,67)(65,68);;
s1 := ( 1,10)( 2,61)( 3,70)( 4,13)( 5, 6)( 7,41)( 8,32)( 9,54)(11,39)(12,35)(14,33)(15,42)(16,21)(17,37)(18,31)(19,38)(20,69)(22,50)(23,66)(24,72)(25,51)(26,58)(27,45)(28,59)(29,48)(30,43)(34,47)(36,46)(40,62)(44,53)(49,55)(52,64)(56,75)(57,77)(60,80)(63,73)(65,76)(67,79)(68,74)(71,78);;
s2 := ( 1,13)( 2,16)( 3,72)( 4,67)( 5,44)( 6,22)( 7,30)( 8,74)( 9,55)(10,80)(11,41)(12,75)(14,26)(15,23)(17,73)(18,20)(19,36)(21,61)(24,49)(25,59)(27,43)(28,60)(29,71)(31,64)(32,48)(33,58)(34,66)(35,68)(37,70)(38,62)(39,57)(40,50)(42,47)(45,76)(46,53)(51,79)(52,69)(54,63)(56,78)(65,77);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(80)!( 1, 5)( 2,41)( 3,32)( 4,54)( 6,43)( 7,18)( 9,14)(10,47)(11,16)(12,64)(13,44)(15,19)(17,62)(20,30)(21,53)(22,27)(23,36)(24,34)(25,29)(26,55)(28,39)(31,75)(33,78)(35,77)(37,76)(38,73)(42,80)(45,70)(46,61)(48,72)(49,66)(51,69)(52,79)(56,58)(57,60)(59,71)(63,67)(65,68);
s1 := Sym(80)!( 1,10)( 2,61)( 3,70)( 4,13)( 5, 6)( 7,41)( 8,32)( 9,54)(11,39)(12,35)(14,33)(15,42)(16,21)(17,37)(18,31)(19,38)(20,69)(22,50)(23,66)(24,72)(25,51)(26,58)(27,45)(28,59)(29,48)(30,43)(34,47)(36,46)(40,62)(44,53)(49,55)(52,64)(56,75)(57,77)(60,80)(63,73)(65,76)(67,79)(68,74)(71,78);
s2 := Sym(80)!( 1,13)( 2,16)( 3,72)( 4,67)( 5,44)( 6,22)( 7,30)( 8,74)( 9,55)(10,80)(11,41)(12,75)(14,26)(15,23)(17,73)(18,20)(19,36)(21,61)(24,49)(25,59)(27,43)(28,60)(29,71)(31,64)(32,48)(33,58)(34,66)(35,68)(37,70)(38,62)(39,57)(40,50)(42,47)(45,76)(46,53)(51,79)(52,69)(54,63)(56,78)(65,77);
poly := sub<Sym(80)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0 >;

References

None.

to this polytope.